RRCD: Program for Constructing Resolvable Row-column Designs

1. Introduction
2. Using RRCD
3. Output
4. Examples
5. References

Introduction

A resolvable row-column design (RCD) is an arrangement of r kxs arrays each of which is a complete replicate of v=ks treatments. We say this resolvable RCD is of size (r,k,s). Chapter 6 of John & Williams (1995) gives an excellent summary of resolvable RCDs. In this note this book is abbreviated as JW.

RRCD is a Gendex module for constructing optimal or near-optimal resolvable RCDs. The approach used by RRCD is to permute the treatments within the blocks of a resolvable incomplete block design (IBD) used as the column component of the RCD. This IBD can be constructed by either the IBD module or the ALPHA module of the Gendex toolkit. The optimality criterion and the algorithm implemented in RRCD are discussed in Nguyen & Williams (1993). In this note this paper is abbreviated as NW.

Using RRCD

Let's assume all Gendex class files are in the directory c:\gendex and suppose you want to construct a resolvable RCD of size (r,k,s)=(2,3,3). The following is the file alpha.txt in the working directory which contains a resolvable IBD of size (v,k,r)=(9,3,2) with blocks as columns (Note: the replicates of a resolvable IBD should be separated by blank lines):

4     8     6
7     2     0
1     5     3

6     3     8
1     7     0
5     2     4

At the working directory, type the following command at the Command Prompt (case is important):

java -cp c:\gendex rrcd

The RRCD window will pop up. Enter alpha.txt at the File text field, the RRCD window will become:

Click START, the OUTPUT window (not shown) displaying the derived resolvable RCD will pop up and the RRCD window will become:

Note that the START button has been changed to the STOP one. If you close the pop-up window, the STOP button will become a RESET one. If you click this RESET button, the output will disappear and you can now start a new design problem. Also note that the default random seed is the one obtained from the system clock and the default number of tries is 100. You can change these default values if you wish to.

Output

The result of the best try is displayed in the OUTPUT wndow and is also saved in the file rrcd.htm in the working directory. This file can be read by a browser such as IE or Netscape. Information for this try includes:

1. Try number;
2. The random seed used;
3. The number of iterations;
4. The objective function f.
5. The row, column and row-column efficiency E of the constructed design and the ratio E/U where U is the upper bound of a resolvable RCD of size (r,k,s). The program automatically stops if this ratio reaches 1.
6. The distribution of the concurrences of this design;
7. The design plan;
8. The time in seconds RRCD used to construct the above design.

An additional output of an RRCD session is the file form.htm. The following is content of file form.htm of the above example:

Rep   Row   Col   Treat
1     1     1     1
1     1     2     2
1     1     3     0
1     2     1     4
1     2     2     5
1     2     3     3
1     3     1     7
1     3     2     8
1     3     3     6
2     1     1     5
2     1     2     7
2     1     3     0
2     2     1     6
2     2     2     2
2     2     3     4
2     3     1     1
2     3     2     3
2     3     3     8

Examples

1. A resolvable RCD of size (r,k,s)=(5,4,4) (http://designcomputing.net/gendex/rrcd/r1.html).
2. A resolvable RCD of size (r,k,s)=(3,4,4) (http://designcomputing.net/gendex/rrcd/r2.html).
3. A resolvable RCD of size (r,k,s)=(4,3,4) (http://designcomputing.net/gendex/rrcd/r3.html).
4. A resolvable RCD of size (r,k,s)=(6,9,7) (http://designcomputing.net/gendex/rrcd/r4.html).
5. A resolvable RCD of size (r,k,s)=(4,4,5) (http://designcomputing.net/gendex/rrcd/r5.html).
6. A resolvable RCD of size (r,k,s)=(2,6,7) (http://designcomputing.net/gendex/rrcd/r6.html).
7. A resolvable RCD of size (r,k,s)=(2,4,7) (http://designcomputing.net/gendex/rrcd/r7.html).
8. A resolvable RCD of size (r,k,s)=(2,5,10) (http://designcomputing.net/gendex/rrcd/r8.html).

Notes:

• Example 1: See JW Example 6.1.
• Example 2: See JW Example 6.2.
• Example 3: See JW Example 6.3.
• Example 4: See JW Example 6.4.
• Example 5: See NW Section 5.
• Example 6: See NW Table 1.
• Example 7: See JW Section 6.6.
• Example 8: See JW Example 6.8.

References

John, J.A. & Williams E.R. (1987) Cyclic designs and computer-generated designs. New York: Chapman & Hall.
Nguyen, N-K & Williams, E.R. (1993) An algorithm for constructing optimal resolvable row-column designs. Austral. J. Statist. 35, 363-370.

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